Simple word problem involving exponents

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Homework Help Overview

The discussion revolves around a word problem involving exponential growth, specifically related to a population of rabbits that triples each month, starting from an initial count of 100 rabbits. Participants are exploring how to formulate equations to determine the population after a set period and to find the time required to reach a specific population size.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the formulation of the exponential growth equation and attempt to express the population mathematically. There is an exploration of how to calculate the population after 4 months and how to determine the time needed to reach 50,000 rabbits.

Discussion Status

Some participants have provided guidance on the mathematical representation of the problem, suggesting the use of an exponential function. There is acknowledgment of the need to use logarithms for one of the questions, indicating a productive direction in the discussion.

Contextual Notes

Participants express uncertainty about how to set up the equations correctly and are navigating through the problem without complete clarity on the steps involved.

danielle36
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A population of rabbits triples every month. Assume we start out with 100 rabbits.

a. How many rabbits are there after 4 months

b. How long until there are 50,000 rabbits?


Homework Equations



... this is where I am running into the trouble... I'm really not sure how to create the equation to solve these problems...


The only attempt I've made at a solution has been

100 * 3 * 3 * 3 * 3 = amount of rabbits after 4 months?

Any help here would be greatly appreciated
 
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So we know that, at time "0", we have 100 rabbits. Every month the population triples (3x).

x(t)=100\times 3^t

t=0

x(t)=100\times 3^0
 
So your questions become

a. How many rabbits are there after 4 months
What is (100)34?

b. How long until there are 50,000 rabbits?
For what t is (100)3t= 50000?

For that last one, you will need to use a logarithm. What is log(3t)?
 
Ahh.. thank you! I had been staring at that problem for way too long without getting anywhere.. now I'm finally unstuck :)
 

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